def rS(n, pi, iters=float('inf'), tol=TOL):
'''
INPUT:
n :: Integer
# number of bins
pi :: NPArray<Float>
# optimal stationary distribution
OUTPUT:
NPArray<NPArray<Float>>
# P^(I) via Random Search Method
# only works in 2x2 case
# BECAUSE IT'S 2x2 CASE I CAN USE 2x2 P^(M) SERIES FORMULA
'''
output = np.zeros([2,2]) # P^(I)
for col in xrange(2):
output[:,col] = np.transpose(genStat(2))
ev = corrEv(output)
b1 = 0.0 if pi[0] >= pi[1] else 1.0-(pi[0]/pi[1])
b2 = 1.0
output[1][1] = np.average([b1,b2])
output = resMat(output)
while not listMatch(np.dot(output, ev), pi, tol=tol) and iters > 0: # s1, loop
output[1][1] = (b2-b1)*np.random.random()+b1
output[0][0] = p22p1(output[1][1], pi) # calculate p_11
output = resMat(output) # calculate p_12, p_21
ev = corrEv(output)
iters -= 1
return output
def GI2(n, pi, maxIters=float('inf'), tol=TOL):
'''
INPUT:
n :: Integer
# number of bins
pi :: NPArray<Float>
# optimal stationary distribution
# CAN'T HAVE ANY ZERO ENTRIES!
OUTPUT:
NPArray<NPArray<Float>>
# P^(I) via Gibbs Sampling-inspired Method
'''
output = np.zeros([n, n]) # P^(I)
for col in xrange(n):
output[:, col] = np.transpose(genStat(n))
ev = corrEv(output)
indices = range(n)
while not listMatch(np.dot(output, ev), pi) and maxIters > 0: # s1, loop
# s2, isolate
alterRow = np.random.choice(indices, size=[2],
replace=False).astype(int)
alterCol = np.random.choice(indices, size=[2],
replace=False).astype(int)
alterRow = np.array([min(alterRow), max(alterRow)
]) # sort in order of lowest to highest
alterCol = np.array([min(alterCol), max(alterCol)
]) # sort in order of lowest to highest
subpi = np.zeros(2)
subpi[0] = pi[alterRow[0]]
subpi[1] = pi[alterRow[1]]
# s3b, note how much space was formerly taken up
resMass_mat = (output[alterRow[0]][alterCol[0]] + output[alterRow[1]][alterCol[0]], \
output[alterRow[0]][alterCol[1]] + output[alterRow[1]][alterCol[1]])
resMass_pi = sum(subpi)
# s3, normalize
subpi /= sum(subpi)
# s4, optimize extracted 2-equation system
submat = brS(n, subpi) # !!! Use bS, rS, brS methods. !!!
# s5a, denormalize
submat[:, 0] *= resMass_mat[0]
submat[:, 1] *= resMass_mat[1]
subpi *= resMass_pi
# s5, substitute in new values renormalized to Q
output[alterRow[0]][alterCol[0]] = submat[0][0]
output[alterRow[1]][alterCol[0]] = submat[1][0]
output[alterRow[0]][alterCol[1]] = submat[0][1]
output[alterRow[1]][alterCol[1]] = submat[1][1]
ev = corrEv(output)
maxIters -= 1
return output
s = sum(pi[cp[0]])
Ai[cp[0][0]:(cp[0][1] + 1),
cp[1][0]:(cp[1][1] + 1)] = brS(2, pi[cp[0]] / s)
A += Ai
output = A / Z
return output, L(output), M(output)
print '\nRUNNING AVG:\n'
errors = []
errors2 = []
b1 = 2
b2 = 11
for i in range(b1, b2):
errors.append(AVG(i, genStat(i))[1])
errors2.append(AVG(i, genStat(i))[2])
e = np.array(errors)
e2 = np.array(errors2)
print e
print e2
print sum(e) / float(b2 - b1)
print sum(e2) / float(b2 - b1)
# errors = []
# errors2 = []
# b = 10
# L = lambda mat, pi: np.linalg.norm(np.dot(mat, pi) - pi)
# M = lambda mat, pi: np.linalg.norm(corrEv(mat) - pi)
# for _ in range(b):
# pi = genStat(2)
subpi[0] = pi[alterRow[0]]
subpi[1] = pi[alterRow[1]]
# s3b, note how much space was formerly taken up
resMass_mat = (output[alterRow[0]][alterCol[0]] + output[alterRow[1]][alterCol[0]], \
output[alterRow[0]][alterCol[1]] + output[alterRow[1]][alterCol[1]])
resMass_pi = sum(subpi)
# s3, normalize
subpi /= sum(subpi)
# s4, optimize extracted 2-equation system
submat = brS(n, subpi) # !!! Use bS, rS, brS methods. !!!
# s5a, denormalize
submat[:, 0] *= resMass_mat[0]
submat[:, 1] *= resMass_mat[1]
subpi *= resMass_pi
# s5, substitute in new values renormalized to Q
output[alterRow[0]][alterCol[0]] = submat[0][0]
output[alterRow[1]][alterCol[0]] = submat[1][0]
output[alterRow[0]][alterCol[1]] = submat[0][1]
output[alterRow[1]][alterCol[1]] = submat[1][1]
ev = corrEv(output)
maxIters -= 1
return output
print GI2(11, genStat(11))
quit()
print '\nRUNNING NOW:\n'
for i in [11]:
print "\n i =", i
print GI2(i, genStat(i))